A seismic station records an earthquake that has a maximum surface wave amplitude of 20 mm and the S-wave arrives 40 seconds after the P-wave. The Richter magnitude of this earthquake is
A) 4.5.
B) 5.
C) 5.5.
D) 6.

Question

Quizplus · Accepted Answer

First, we can use the time difference between the P-wave and S-wave to determine the distance between the seismic station and the epicenter of the earthquake. Since S-waves travel slower than P-waves, the time difference tells us how long it took for the S-wave to travel the extra distance.

Using the equation: 
distance = rate x time

And assuming P-waves and S-waves travel at different speeds: 
distance = (speed of S-wave - speed of P-wave) x time 
distance = (3.5 - 6.0) km/s x 40 s 
distance = 86 km

Next, we can use the maximum surface wave amplitude to determine the Richter magnitude using the following equation: 
magnitude = log(amplitude) + 1.5log(distance) - 3

Plugging in the values: 
magnitude = log(20 mm) + 1.5log(86 km) - 3 
magnitude = 5.5

Therefore, the answer is C) 5.5.

A Seismic Station Records an Earthquake That Has a Maximum